Question
The number of functions f: \ 1, 2, 3, 4\ \ a, b, c\ , which are not onto, is:
JEE Main
Mathematics
Functions
2026
JEE Main 2026 (04 April Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 48
- B. 45
- C. 51
- D. 35
Answer
B. 45
Step-by-step solution
Total number of functions from a set of 4 elements to a set of 3 elements is 3^4 = 81. The number of onto functions is given by the inclusion-exclusion principle: 3^4 - ^ 3 C_ 1 2^4 + ^ 3 C_ 2 1^4 = 81 - 3 16 + 3 1 = 81 - 48 + 3 = 36 The number of functions which are not onto is the total number of functions minus the number of onto functions: 81 - 36 = 45 Answer: 45
Related: Mathematics — Functions · All PYQ Banks